Gibbs Adsorption Isotherm
Gibbs derived a thermodynamic relationship between the surface or interfacial tension γ and the surface excess Γ (adsorption per unit area). At constant temperature, in the presence of adsorption, the Gibbs adsorption equation is dγ = −∑(ni/A)dμI = −∑ΓidμI, where (ni/A) = Γi is the number of moles of component I adsorbed per unit area and μI is the chemical potential of the surfactant solution. For a single surfactant component, the Gibbs adsorption equation is simply dγ/dlog C = −2.303 Γ RT, where C is the surfactant concentration, R is the gas constant, and T is the absolute temperatures. The Gibbs adsorption equation allows one to determine the amount of surfactant adsorption Γ (moles m−2) from a plot of log γ (the surface tension at the air/water interface or interfacial tension at the liquid/liquid interface) versus log C. The results show a linear decrease of log γ with log C at concentrations just below the surfactant critical micelle...